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Teaching Mixed Numbers and Improper Fractions

Updated: Aug 22, 2021

Once students understand regular fractions (aka "proper fractions"), the next leap is mastering improper fractions and mixed numbers. I emphasize to my third grade students that regular fractions are always less than a whole, and mixed numbers/improper fractions are more than a whole. Like fractions, it's good for students to see mixed numbers in a variety of ways. Here are some teaching resources to model mixed numbers with both real life examples and fraction models!

1. Identify Real World Mixed Numbers

Make fractions real to students by showing them lots of different real world examples! Using concrete objects like food, stickers, and play dough makes fractions relatable and fun. I made a 15-slide powerpoint with real, color photos of food and objects that can be described using mixed numbers. Each slide clearly defines what is one whole before asking the question. Example: "If one dozen donuts equals one whole, describe these doughnuts as a mixed number". This is a great activity to provide elementary students with concrete visuals to help them understand mixed numbers. This teaching resource also includes a PDF and Google Slides version to assist with virtual learning needs.

Picture of Reese's peanut butter cups. There are 5 whole chocolates and one half of a chocolate.

2. Make Fraction Models with Virtual Manipulatives

This website from NCTM (National Council of Teachers of Mathematics) allows you to create a model and labels it four different ways: improper fraction, mixed number, decimal, and percent. (You can click on where it says "Area" in the lower right-hand corner to change the type of models).

Two and one fourth modeled with squares on website using fraction models

You can also use virtual manipulatives on to model mixed numbers and improper fractions. If you click on the gear icon, you can change the fraction strips to circle fraction models.

One and a half and three halves modeled with fraction strips on website using virtual fraction strips

3. Color Models of Mixed Numbers and Improper Fractions

These practice pages provide another format for elementary kids to practice modeling improper fractions and mixed numbers. The blank models provide scaffolding (easier than drawing the shapes yourself!) so students simply need to color in the correct amount of fractional pieces to model each mixed number or improper fraction. Simple but effective! You can peek over a student's shoulder and see whether or not they understand the concepts. These are also great remediation for students who need more practice with the concepts.

4. Make a Fraction Picture

This free resource is inspired by Ed Emberley's book Picture PIe. The full circle equals one whole and there are templates included in the resource for halves, fourths, and eighths. Students can use their creativity to make a picture out of the fraction pieces, and then describe their picture using a mixed number. This could also be great for a bulletin board or classroom display!

Student work examples of fraction pictures

What strategies help you teach mixed numbers and improper fractions? I'd love to hear your ideas!

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